Analysis of Damage and Plasticity for Large Deformation with Application in Simple Shear

Abstract

A coupled theory of continuum damage mechanics and finite strain plasticity is formulated in the Eulerian reference system. A linear transformation is shown to exist between the effective deviatoric Cauchy stress tensor and the total Cauchy stress tensor. In addition, an effective elasto-plastic stiffness tensor is derived that includes the effects of damage. The problem of finite simple shear is investigated. It is noticed that the resulting differential equations are solved numerically using a Runge-Kutta-Verner fifth order and sixth order method. The results for the stress, backstress and damage variables are compared with a previous damage theory by the authors, as well as with an undamaged plasticity model.